Either you can change the screen bindings or you can change the bindings of your shell. Assuming your shell is bash, the output of bind -p | grep \C-a should give you the current action binded to Ctrl+A. To bind this action to something else use the following form:

$ bind '"\C-p": beginning-of-line'

This will bind Ctrl+P to move the cursor to the beginning of the line. Remember the double-quotes inside the expression. To unset a binding you would just set it to nothing:

$ bind '"\C-a": '

To list all input sequences associated with the action, use:

$ bind -p | grep beginning-of-line

Lastly, to make the bindings permament you can put the statements in your ~/.bashrc file and issue source ~/.bashrc.